Related papers: Numerical Stability of Generalized Entropies
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based…
An analytical expression of probability density function (PDF) of velocity fluctuation is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the R\'{e}nyi entropy). It is revealed that the derived…
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as positivity and compatibility with the discrete case. In this…
The class of SPA entropies, which can be represented as an increasing continuous transformation of Shannon and R\'enyi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been…
A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…
More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics.…
The Tsallis and R\'enyi entropies are important quantities in the information theory, statistics and related fields because the Tsallis entropy is an one parameter generalization of the Shannon entropy and the R\'enyi entropy includes…